EXP016 · Powers, exponents & logarithms · Classes 9–12
Common Logarithm (base 10)
The common logarithm log x asks: 10 to what power gives x? It turns multiplication by 10 into adding 1.
log xCommon Logarithm (base 10)
📐 Formula
log₁₀ x = y ⇔ 10ʸ = x
✏️ Worked example
log 1000 = 3 because 10³ = 1000.
🌍 Where it is used
Decibels for sound, the pH scale and the Richter scale for earthquakes.
❓ Quick check
log 0.01 = ?
🏋️ Practice
Easylog 100 = ?
Answer: 2
Mediumlog 1 = ?
Answer: 0
ChallengeIf log x = 2.5, between which two whole numbers of hundreds is x?
Answer: 300 and 400 (x ≈ 316)